FastTrack$$ Bikes, Inc. is thinking of developing a new composite road bike. Development will take $6$ years and the cost is $ $195$ comma $500$ per year. Once in$$ production, the bike is expected to make $$$$300$ comma $400$ per year for $10$ years. The cash inflows begin at the end of year $7.$

Assume the cost of capital is $10\mathrm{.}6\%$ for parts $($a$),($b$),$ and $($c$)$ below.

a$.$ Calculate the NPV of this investment opportunity. Should the company make the$$ investment?

b$.$ Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

c$.$ With costs remaining at $ $195$ comma $500$ per$$ year, how long must development last to change the$$ decision?

Assume the cost of capital is $13\mathrm{.}1\%$ for parts $($d$),($e$),$ and $($f$)$ below.

d$.$ Calculate the NPV of this investment opportunity. Should the company make the$$ investment?

e$.$ How much must this cost of capital estimate deviate to change the$$ decision?

f$.$ With costs remaining at $ $195$ comma $500$ per$$ year, how long must development last to change the$$ decision?